Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 1 (P1-9709/01) | Year 2020 | Feb-Mar | (P1-9709/12) | Q#8
A woman’s basic salary for her first year with a particular company is $30000 and at the end of the year she also gets a bonus of $600.
a)For her first year, express her bonus as a percentage of her basic salary.
At the end of each complete year, the woman’s basic salary will increase by 3% and her bonus will increase by $100.
b)Express the bonus she will be paid at the end of her 24th year as a percentage of the basic salary paid during that year.
From the given information, we can collect following information.
The basic salary for her first year;
The bonus at the end of first year;
Her bonus as percentage of her salary;
Her bonus is 2% of her first year’s salary.
Salary of 1st year;
Since annual rate of growth continues to be constant at 3%.
Salary of 2nd year;
Similarly, salary of 3rd year will be;
Hence, salary for 4th year will be;
It is evident that this model represents Geometric Progression (G.P).
Now, we find her salary on 24th year.
Expression for the general term in the Geometric Progression (G.P) is:
We can find the common ratio as follows.
Expression for Common Ratio () in a Geometric Progression (G.P) is;
Her bonus on 24th year will be;
Finally, we can express this bonus as percentage of 24th year’s salary;